System and method of automotive production planning

ABSTRACT

A system and method are disclosed including a production planner that receives a sales forecast for configurations of an automobile. The demand planner also receives constraints associated with an automobile supply chain. The demand planner further models configurations and constraints as a mixed integer linear programming problem, determines a production plan for automobiles, and sends instructions to cause automated machinery to retrieve an amount of automobiles equal to a forecasted production level minus a current inventory level and to move the amount of the automobile to an inventory location of the automobile.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/621,525, filed on Jun. 13, 2017, entitled “System and Method ofAutomated Production Planning,” which claims the benefit under 35 U.S.C.§ 119(e) to U.S. Provisional Application No. 62/361,118, filed Jul. 12,2016, and entitled “System and Method of Automated Production Planning.”U.S. patent application Ser. No. 15/621,525 and U.S. ProvisionalApplication No. 62/361,118 are assigned to the assignee of the presentapplication. The subject matter disclosed in U.S. patent applicationSer. No. 15/621,525 and U.S. Provisional Application No. 62/361,118 ishereby incorporated by reference into the present disclosure as if fullyset forth herein.

TECHNICAL FIELD

The present disclosure relates generally to automotive productionplanning and specifically to a system and method of determiningallocation of automobile configuration production in a multi-plantmulti-market multi-period supply chain.

BACKGROUND

Automobiles (such as cars, trucks, and other types of motorizedvehicles) are typically sold in various configurations. Eachconfiguration can have hundreds or thousands of different options. Forexample, a car may be sold in different trims, such as a sport model,economy model, premium model, or the like. Each of the models may have adifferent type of engine, radio, upholstery, lighting, or othercomponents. Some of the components may always be sold together in thesame configuration while others may never be sold in the sameconfiguration. The configurations of the many components of the typicalautomobile makes determining an automotive production plan difficult.The complexity to determine automobile production with so manyconfigurations is undesirable.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention may be derived byreferring to the detailed description when considered in connection withthe following illustrative figures. In the figures, like referencenumbers refer to like elements or acts throughout the figures.

FIG. 1 illustrates an exemplary supply chain network according to afirst embodiment;

FIG. 2 illustrates the production planner of FIG. 1 in greater detail,in accordance with an embodiment;

FIG. 3 illustrates an exemplary method of automobile configurationplanning according to an embodiment;

FIG. 4 illustrates a graphical representation of a network model of theautomobile supply chain network, according to an embodiment;

FIG. 5 illustrates the flow of production of a single automobile modelthrough the exemplary network model of FIG. 4, according to anembodiment;

FIG. 6 illustrates the flow of production of two automobile modelsthrough the exemplary network model of FIG. 4, according to anembodiment;

FIG. 7 illustrates the flow of production of two automobile models withthree configurations through the exemplary network model of FIG. 4,according to an embodiment;

FIG. 8 illustrates a linear equation matrix of the completewell-structured MIP model of the automotive supply chain network,according to an embodiment; and

FIG. 9 illustrates the structure of the linear equation matrix of thecomplete well-structured MIP model of the automotive supply chainnetwork, according to an embodiment.

DETAILED DESCRIPTION

Aspects and applications of the invention presented herein are describedbelow in the drawings and detailed description of the invention. Unlessspecifically noted, it is intended that the words and phrases in thespecification and the claims be given their plain, ordinary, andaccustomed meaning to those of ordinary skill in the applicable arts.

In the following description, and for the purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of the various aspects of the invention. It will beunderstood, however, by those skilled in the relevant arts, that thepresent invention may be practiced without these specific details. Inother instances, known structures and devices are shown or discussedmore generally in order to avoid obscuring the invention. In many cases,a description of the operation is sufficient to enable one to implementthe various forms of the invention, particularly when the operation isto be implemented in software. It should be noted that there are manydifferent and alternative configurations, devices and technologies towhich the disclosed inventions may be applied. The full scope of theinventions is not limited to the examples that are described below.

As described more fully below, aspects of the following disclosurerelate to production planning of automobile configurations in amulti-plant multi-market multi-period automobile supply chain network.Automobiles (such as cars, trucks, and other types of motorizedvehicles) are typically sold with the presence or absence of variouscomponents substituted for one another. The presence, absence, orsubstitution of any components may be termed as an “option.” A typicalautomobile may comprise hundreds or thousands of options, which may besold as various combinations of options, or configurations. For example,a particular automobile model may be sold in various types of trim, suchas a sports trim, economy trim, mid-range trim, premium trim, or thelike. Examples of automobile models are sports utility vehicle (SUV),station wagon, sedan, coupe, hatchback, electric, and the like. Each ofthe automobile models may be associated with available options such as aspecific type of engine (e.g. V8, V6, four cylinder), radio (e.g. AM/FMradio, satellite radio, touchscreen interface, navigation equipment),upholstery (e.g. fabric, leather, race-style seating), lighting (e.g.fog lamps, HID lights, LED lights, projector headlights), or other likeoptions. Some of the options may be interdependent such that someoptions must always be included together, some options may never beincluded together, and some options may or may not be included in thesame configuration.

In addition, selecting automobile configurations may be dependent onmore than just the interdependency of options. Selecting such aconfiguration may be dependent on demand, capacity and othermanufacturing and logistical constraints, lead time, supply chaindisruption, lot sizes, and other factors. Such factors play a crucialrole in configuration decisions such as adding or removing options froma configuration or whether to introduce a new configuration.

The automobile industry has used many techniques to optimize productionplanning of automobile configurations including just in time, build toorder, and other techniques. However, embodiments of the currentdisclosure solve production planning for automobile configurations froma higher-level perspective. Some embodiments employ a network model, amixed-integer linear problem (MIP) with variable aggregation, and awell-structured MIP model for large-scale automotive production planningcomprising three sub-models: a network production sub-model, an optioncapacity model, and a linking constraints model. According toembodiments, production plans based, at least in part, on one or more ofthese models may be generated from high-level inputs of automobile,manufacturing plant, market, and period information.

FIG. 1 illustrates an exemplary supply chain network 100 according to afirst embodiment. Supply chain network 100 comprises production planner110, one or more imagers 120, third party logistics 130, automobilesuppliers 140, automobile manufacturers 150, automobile distributors160, automobile dealerships 170, computer 180, network 190, andcommunication links 191-198. Although a single production planner 110,one or more imagers 120, one or more third party logistics 130, one ormore automobile suppliers 140, one or more automobile manufacturers 150,one or more automobile distributors 160, one or more automobiledealerships 170, a single computer 180, and a single network 190 areshown and described, embodiments contemplate any number of productionplanners, imagers, third party logistics, automobile suppliers,automobile manufacturers, automobile distributors, automobiledealerships, computers, and networks, according to particular needs.

In one embodiment, production planner 110 comprises server 112 anddatabase 114. According to embodiments, production planner 110 receivesa demand or production forecast for vehicle model and options anddetermines a quantity and configuration of automobiles to be produced.Production planning may comprise a holistic approach that considers manyor all aspects of a production planning problem by modeling theproduction plan as, for example, a linear program. Production planner110 may then determine a quantity and configuration of automobiles to beproduced by which manufacturing plants, for which markets, at which timeperiods based on automobile supply chain constraints and possibleautomobile configurations.

Automobile supply chain constraints used in the production planningproblem may include, for example, flow constraints (i.e. the number ofautomobiles entering a node equals the number of automobiles leaving anode, or the total of starting stock and production equals the total ofsales and ending stock), manufacturing plant constraints (e.g. capacity,lead time, and diversity), supplier capacity constraints, and minimumand maximum stock constraints. Each automobile configuration may berepresented in the production plan by a serial number, code, or otheralphanumeric string representing one or more, or all, of the possibleoptions for an automobile configuration.

One or more imagers 120 comprise one or more electronic devices thatreceive imaging information from one or more sensors 126 or from one ormore databases in supply chain network 100. According to embodiments,one or more imagers 120 comprise one or more processors 122, memory 124,one or more sensors 126, and may include any suitable input device,output device, fixed or removable computer-readable storage media, orthe like. According to embodiments, one or more imagers 120 identifyitems near the one or more sensors 126 and generate a mapping of theitem in supply chain network 100. As explained in more detail below, oneor more third party logistics 130, suppliers 140, manufacturers 150,distributors 160, and dealerships 170 use the mapping of an item tolocate the item in the supply chain network 100. The location of theitem is then used to coordinate the storage and transportation of itemsin supply chain network 100 to implement one or more plans generated byproduction planner 110. Plans may comprise one or more of a productionplan, demand plan, option plan, sales and operation plan, and masterplan, as described herein.

One or more imagers 120 may comprise a mobile handheld device such as,for example, a smartphone, a tablet computer, a wireless device, or thelike. In addition, or as an alternative, one or more imagers 120comprise one or more networked electronic devices configured to transmititem identity information to one or more databases as an item passes byor is scanned by one or more imagers 120. This may include, for example,a stationary scanner located at one or more third party logistics 130,suppliers 140, manufacturers 150, distributors 160, or dealerships 170that identifies items as the items pass near the scanner, including inone or more transportation vehicles 136. One or more sensors 126 of oneor more imagers 120 may comprise an imaging sensor, such as, a camera,scanner, electronic eye, photodiode, charged coupled device (CCD), orany other electronic or manual sensor that detects or identifies imagesof automobiles or automotive components or reads labels, barcodes, orthe like coupled with automobiles or automotive components. In addition,or as an alternative, one or more sensors 126 may comprise a radioreceiver and/or transmitter configured to read an electronic tag coupledwith an automobile or automotive component, such as, for example, anRFID tag.

Third party logistics 130 comprises server 132 and database 134.According to embodiments, third party logistics 130 directs one or moretransportation vehicles 136 to ship one or more items between one ormore third party logistics 130, suppliers 140, manufacturers 150,distributors 160, or dealerships 170, based, at least in part, on thequantities of a production plan determined by production planner 110.Transportation vehicles 136 comprise, for example, any number of trucks,cars, vans, boats, airplanes, unmanned aerial vehicles (UAVs), cranes,robotic machinery, or the like. In addition to the production plan, thenumber of items shipped by transportation vehicles 136 in third partylogistics 130 may also be based, at least in part, on the number ofitems currently in stock at one or more third party logistics 130,suppliers 140, manufacturers 150, distributors 160, or dealerships 170,the number of items currently in transit, forecasted demand, a supplychain disruption, and the like. According to embodiments, transportationvehicles 136 may be associated with one or more suppliers 140,manufacturers 150, distributors 160, or dealerships 170, or anothersupply chain entity, according to particular needs.

As shown in FIG. 1, supply chain network 100 operates on one or morecomputers 180 that are integral to or separate from the hardware and/orsoftware that support production planner 110 and one or more imagers120, third party logistics 130, suppliers 140, manufacturers 150,distributors 160, and dealerships 170. Supply chain network 100comprising production planner 110 and one or more imagers 120, thirdparty logistics 130, suppliers 140, manufacturers 150, distributors 160,and dealerships 170 may operate on one or more computers 180 that areintegral to or separate from the hardware and/or software that supportthe production planner 110 and one or more imagers 120, third partylogistics 130, suppliers 140, manufacturers 150, distributors 160, anddealerships 170. Computers 180 may include any suitable input device182, such as a keypad, mouse, touch screen, microphone, or other deviceto input information. Output device 184 may convey informationassociated with the operation of supply chain network 100, includingdigital or analog data, visual information, or audio information.

Computer 180 may include fixed or removable computer-readable storagemedia, including a non-transitory computer readable medium, magneticcomputer disks, flash drives, CD-ROM, in-memory device or other suitablemedia to receive output from and provide input to supply chain network100. Computer 180 may include one or more processors 186 and associatedmemory to execute instructions and manipulate information according tothe operation of supply chain network 100 and any of the methodsdescribed herein. In addition, or as an alternative, embodimentscontemplate executing the instructions on computer 180 that causecomputer 180 to perform functions of the method. Further examples mayalso include articles of manufacture including tangiblecomputer-readable media that have computer-readable instructions encodedthereon, and the instructions may comprise instructions to performfunctions of the methods described herein. According to someembodiments, the functions and methods described in connection withimager 120 may be emulated by one or more modules configured to performthe functions and methods as described.

Production planner 110 and one or more imagers 120, third partylogistics 130, suppliers 140, manufacturers 150, distributors 160, anddealerships 170 may each operate on one or more separate computers, anetwork of one or more separate or collective computers, or may operateon one or more shared computers. In addition, supply chain network 100may comprise a cloud based computing system having processing andstorage devices at one or more locations, local to, or remote fromproduction planner 110 and one or more imagers 120, third partylogistics 130, suppliers 140, manufacturers 150, distributors 160, anddealerships 170. In addition, each of the one or more computers 180 maybe a work station, personal computer (PC), network computer, notebookcomputer, tablet, personal digital assistant (PDA), cell phone,telephone, smartphone, mobile device, wireless data port, augmented orvirtual reality headset, or any other suitable computing device. In anembodiment, one or more users may be associated with production planner110 and one or more imagers 120, third party logistics 130, suppliers140, manufacturers 150, distributors 160, and dealerships 170. These oneor more users may include, for example, a “manager” or a “planner”handling production planning and/or one or more related tasks withinsupply chain network 100. In addition, or as an alternative, these oneor more users within supply chain network 100 may include, for example,one or more computers programmed to autonomously handle, among otherthings, production planning, demand planning, option planning, sales andoperations planning, order placement, automated warehouse operations(including removing automobile components from and placing automobilecomponents in inventory), robotic production machinery (includingbuilding or assembling automobiles or automobile components), and/or oneor more related tasks within supply chain network 100.

One or more third party logistics 130, suppliers 140, manufacturers 150,distributors 160, and dealerships 170 represent one or more automotivesupply chain entities in one or more supply chain networks 100,including one or more enterprises. One or more third party logistics 130may be any suitable entity that provides warehousing and transportationfor automobile or automotive components in the automobile supply chain.Third party logistics 130 may, for example, receive an automobile orautomotive component from a supply chain entity in the supply chainnetwork and store and transport the automobile or automotive componentfor another supply chain entity. One or more third party logistics 130may comprise automated warehousing systems that automatically removeautomobile components from and place automobile components intoinventory based, at least in part, on a production plan, demand plan,option plan, sales and operation plan, or master plan determined byproduction planner 110. Automotive components may comprise, for example,components, materials, products, parts, items, or supplies that may beused to produce automobiles or other automotive components. In addition,or as an alternative, an automotive component may comprise a part of theautomobile or a supply or resource that is used to manufacture theautomobile, but does not become a part of the automobile.

One or more suppliers 140 may be any suitable entity that offers to sellor otherwise provides one or more automotive components to one or moreautomotive manufacturers 150. Suppliers 140 may comprise automateddistribution systems 142 that automatically transport automobiles andautomotive components to one or more automotive manufacturers 150 based,at least in part, on a production plan, demand plan, option plan, salesand operation plan, or master plan determined by production planner 110and/or one or more other factors described herein.

Automobile manufacturer 150 may be any suitable entity that manufacturesat least one automobile or automotive component. Manufacturer 150 mayuse one or more automotive components during the manufacturing processto manufacture, fabricate, assemble, or otherwise process an automobileor automotive component. An automobile or automotive component may besupplied to another automobile manufacturer 150, third party logistics130, supplier 140, distributor 160, and/or dealership 170 in theautomobile supply chain network 110. Automobile manufacturer 150 may,for example, produce and sell an automobile or automotive component tosupplier 140, another manufacturer 150, a distributor 160, dealership,170 a customer, or any other suitable person or entity. Such automobilemanufacturers 150 may comprise automated robotic production machinery152 that produces automobiles and automobile components based, at leastin part, on a production plan, demand plan, option plan, sales andoperation plan, or master plan determined by production planner 110.

Distributor 160 may be any suitable entity that offers to sell orotherwise distributes at least one automobile or automotive component toone or more dealerships 170 and/or customers. Distributors 160 may, forexample, receive a product from a first automotive supply chain entityin supply chain network 100 and store and transport the product for asecond automotive supply chain entity. Such distributors 160 maycomprise automated warehousing systems 162 that automatically transportto one or more dealerships 170 or customers and/or automatically removefrom or place into inventory automobiles and automobile componentsbased, based, at least in part, on a production plan, demand plan,option plan, sales and operation plan, or master plan determined byproduction planner 110. One or more dealerships 170 may be any suitableentity that obtains one or more automobiles or automotive component tosell to one or more customers. In addition, one or more dealerships 170may sell, store, and supply one or more automotive components and/orrepair an automobile with one or more automotive components. One or moredealerships 170 may comprise any online or brick and mortar location,including locations with shelving systems 172. Shelving systems 172 maycomprise, for example, various racks, fixtures, brackets, notches,grooves, slots, or other attachment devices for fixing shelves invarious configurations. These configurations may comprise shelving withadjustable lengths, heights, and other arrangements, which may beadjusted by an employee of one or more dealerships 170 based oncomputer-generated instructions or automatically by machinery to placeautomobiles or automotive components in a desired location.

Although one or more third party logistics 130, suppliers 140,manufacturers 150, distributors 160, and dealerships 170 are shown anddescribed as separate and distinct entities, the same entity maysimultaneously act as any one or more third party logistics 130,suppliers 140, manufacturers 150, distributors 160, and dealerships 170.For example, one or more automobile manufacturers 150 acting as amanufacturer could produce an automobile or automotive component, andthe same entity could act as a supplier to supply an automobile orautomotive component to another automotive supply chain entity. Althoughone example of a supply chain network 100 is shown and described;embodiments contemplate any configuration of supply chain network 100,without departing from the scope of the present disclosure.

In one embodiment, production planner 110 may be coupled with network190 using communications link 191, which may be any wireline, wireless,or other link suitable to support data communications between productionplanner 110 and network 190 during operation of supply chain network100. One or more imagers 120 are coupled with network 190 usingcommunications link 192, which may be any wireline, wireless, or otherlink suitable to support data communications between one or more imagers120 and network 190 during operation of distributed supply chain network100. Third party logistics 130 may be coupled with network 190 usingcommunications link 193, which may be any wireline, wireless, or otherlink suitable to support data communications between third partylogistics 130 and network 190 during operation of supply chain network100.

One or more suppliers 140 may be coupled with network 190 usingcommunications link 194, which may be any wireline, wireless, or otherlink suitable to support data communications between one or moresuppliers 140 and network 190 during operation of supply chain network100. One or more manufacturers 150 may be coupled with network 190 usingcommunications link 195, which may be any wireline, wireless, or otherlink suitable to support data communications between one or moremanufacturers 150 and network 190 during operation of supply chainnetwork 100. One or more distributors 160 may be coupled with network190 using communications link 196 which may be any wireline, wireless,or other link suitable to support data communications between one ormore distributors 160 and network 190 during operation of supply chainnetwork 100. One or more dealerships 170 may be coupled with network 190using communications link 197, which may be any wireline, wireless, orother link suitable to support data communications between one or moredealerships 170 and network 190 during operation of supply chain network100. Computer 180 may be coupled with network 190 using communicationslink 198, which may be any wireline, wireless, or other link suitable tosupport data communications between computer 180 and network 190 duringoperation of supply chain network 100.

Although communication links 191-198 are shown as generally couplingproduction planner 110 and one or more imagers 120, third partylogistics 130, suppliers 140, manufacturers 150, distributors 160,dealerships 170, and computer 180 to network 190, each of productionplanner 110 and one or more imagers 120, third party logistics 130,suppliers 140, manufacturers 150, distributors 160, dealerships 170, andcomputer 180 may communicate directly with each other, according toparticular needs.

In another embodiment, network 190 includes the Internet and anyappropriate local area networks (LANs), metropolitan area networks(MANs), or wide area networks (WANs) coupling production planner 110 andone or more imagers 120, third party logistics 130, suppliers 140,manufacturers 150, distributors 160, dealerships 170, and computer 180.For example, data may be maintained by locally or externally ofproduction planner 110 and one or more imagers 120, third partylogistics 130, suppliers 140, manufacturers 150, distributors 160,dealerships 170, and computer 180 and made available to one or moreassociated users of production planner 110 and one or more imagers 120,third party logistics 130, suppliers 140, manufacturers 150,distributors 160, dealerships 170, and computer 180 using network 190 orin any other appropriate manner. For example, data may be maintained ina cloud database at one or more locations external to production planner110 and one or more imagers 120, third party logistics 130, suppliers140, manufacturers 150, distributors 160, dealerships 170, and computer180 and made available to one or more associated users of productionplanner 110 and one or more imagers 120, third party logistics 130,suppliers 140, manufacturers 150, distributors 160, dealerships 170, andcomputer 180 using the cloud or in any other appropriate manner. Thoseskilled in the art will recognize that the complete structure andoperation of network 190 and other components within supply chainnetwork 100 are not depicted or described. Embodiments may be employedin conjunction with known communications networks and other components.

In accordance with the principles of embodiments described herein,production planner 110 and/or one or more automotive supply chainentities may generate one or more supply chain plans, including aproduction plan, a demand plan, an option plan, a sales and operationplan, and a master plan, and modify the supply chain based on thegenerated plans. For example, according to some embodiments, productionplanner 110 automatically places orders for automobile or automotivecomponents at one or more suppliers 140, manufacturers 150, ordistributors 160, initiates manufacturing of the automobile orautomotive components at one or more manufacturers 150, and determinesautomobile or automotive components to be carried at one or moredealerships 170. Furthermore, production planner 110 may instructautomated machinery (i.e., robotic warehouse systems, robotic inventorysystems, automated guided vehicles, mobile racking units, automatedrobotic production machinery, robotic devices and the like) to adjustproduct mix ratios, inventory levels at various stocking points,production of products of manufacturing equipment, and proportional oralternative sourcing of one or more third party logistics 130, suppliers140, manufacturers 150, distributors 160, and dealerships 170 based onone or more generated plans and/or current inventory or productionlevels. For example, the methods described herein may include computers180 receiving product data from automated machinery having at least onesensor and the product data corresponding to an item detected by theautomated machinery. The received product data may include an image ofthe item, an identifier, as described above, and/or other product dataassociated with the automobile or automotive component (dimensions,texture, estimated weight, and any other like attributes). The methodmay further include computers 180 looking up the received product datain database 114 associated with production planner 110 to identify theitem corresponding to the product data received from the automatedmachinery.

Computers 180 may also receive, from the automated machinery, a currentlocation of the identified automobile or automotive component. Based onthe identification of the automobile or automotive component, computers180 may also identify (or alternatively generate) a first mapping in thedatabase system, where the first mapping is associated with the currentlocation of the identified automobile or automotive component. Computers180 may also identify a second mapping in the database system, where thesecond mapping is associated with a past location of the identifiedautomobile or automotive component. Computers 180 may also compare thefirst mapping and the second mapping to determine if the currentlocation of the identified automobile or automotive component in thefirst mapping is different than the past location of the identifiedautomobile or automotive component in the second mapping. Computers 180may then send instructions to the automated machinery based, as least inpart, on one or more differences between the first mapping and thesecond mapping such as, for example, to locate automobile or automotivecomponent to add to or remove from an inventory of one or more thirdparty logistics 130, suppliers 140, manufacturers 150, distributors 160,and dealerships 170.

FIG. 2 illustrates production planner 110 of FIG. 1 in greater detail,in accordance with an embodiment. As discussed above, production planner110 may comprise server 112 and database 114. Although productionplanner 110 is shown and described as comprising a single server 112 anddatabase 114, embodiments contemplate any suitable number of servers ordatabases internal to or externally coupled with production planner 110.In addition, or as an alternative, a production planner may be locatedinternal or external to the one or more third party logistics 130,suppliers 140, manufacturers 150, distributors 160, and dealerships 170according to particular needs.

According to embodiments, server 112 of production planner 110 maycomprise production planning engine 202, demand engine 204, optionengine 206, sales and operations engine 208, master planner 210, andmodeler 212. In addition, database 114 of production planner 110comprises a configuration database 220 (which comprises options data222, option constraints 224, configuration data 226, and hierarchy data228), sales forecast data 230, production capacity data 232, inventorydata 234, time period data 236, manufacturer data 238, market data 240,option production constraints 242, and models 244. Although particularengines, planners, modelers, and databases are shown and described,embodiments contemplate any suitable number or combination of engines,planners, modelers, and databases located at one or more locations,local to, or remote from, production planner 110, according toparticular needs. Furthermore, the engines, planners, modelers, anddatabases may be located at one or more locations, local to or remotefrom, production planner 110 such as on multiple servers or computers atany location in the supply chain network, such as networked among one ormore third party logistics 130, suppliers 140, manufacturers 150,distributors 160, and dealerships 170.

Production planning engine 202 of server 112 may determine a productionplan based, at least in part, on one or more constrained orunconstrained plans received from demand planning engine 204, optionplanning engine 206, and/or sales and operations planning engine 208.For example, production planner 110 may reconcile the option plan fromoption engine 206 according to the demand plan received from demandplanning engine 204 and the sales and operations plan received fromsales and operation engine 208, iteratively, to generate a productionplan. In other words, production planner 110 may receive the demandplan, option plan, and sales and operations plan and refine each of theplans iteratively to generate a production plan.

According to embodiments, production planner 110 generates a productionplan based, at least in part, on automobile configurations (includingpredefined vehicle configurations, which may be referred to as“predefined automobiles”), historical and forecast sales data 230,production capacity data 232, inventory data 234, time period data 235,manufacturer data 238, market data 240, option production constraints242, and any other constraints in accordance with one or more models244. The predefined automobiles may comprise, for example, a list ofautomobile configurations which may include a demand associated withparticular options, configurations, or fully defined vehicles (FDV), asdescribed in more detail below. Historical and forecast sales data 230may comprise, for example, past and projected demand of sales organizedaccording to any particular criteria, including automobile models,automobile options, automobile configurations, components, automobiles,markets, periods, and the like.

Production capacity data 232 may comprise data establishing the minimumand maximum capacity for production of one or more manufacturers 150 forautomobile or automobile components over a given time period and may beassociated with a lead time. Inventory data 234 may comprise the minimumand maximum number of automobiles models or automobile components thatmay be stored at various stocking points in the supply chain as well asthe current or projected stock at each stocking point. According toembodiments, production planning engine 202 receives and transmitsinventory data 234, including item identifiers, pricing data, attributedata, inventory levels, and other like data about one or moreautomobiles or automotive components between one or more locations inthe supply chain network 100 including among one or more third partylogistics 130, suppliers 140, manufacturers 150, distributors 160, anddealerships 170.

Time period data 236 may comprise, for example, any suitable timeinformation, such as a planning period of weeks, months, days, years,quarter, or any other suitable time period over which one or more planis determined. Importantly, time period information may be especiallycritical to the functionality of production planner 110 where aproduction planner may need to consider inputs over a long time period,such as, for example, between one and two years, or longer. Manufacturerdata 238 may comprise data relating to the manufacturing plants forautomobile or automobile components such as the markets served by eachmanufacturer 150, the distribution chains for each manufacturer 150, andthe types of automobile and automobile components that may bemanufactured at each manufacturer 150. Market data 240 may comprise datadelineating the regions (geographic, economic, or otherwise) that areused to model distribution of automobile or automobile components.

Manufacturer data 238 and market data 240 may comprise, for example, thenumber, type, and location of automobile manufacturers 150 and themarkets that those manufacturers 150 serve. For example, manufacturers150 may be associated with a particular region where the manufacturer150 operates, such as, the United States, Canada, Mexico, Europe, or anyother geographical region, such as a state, country, or continent.Similarly, markets may be divided into any desired geographical region,such as by state, country, continent, or any other region. Markets maycomprise, for example, the Americas, Europe, and Asia, or markets maycomprise the United States, Mexico, and Canada. Any other combination ofmanufacturing plant and market information may be organized into anydesired region, according to particular needs. Option productionconstraints 242 are related to the capability of the manufacturers 150to produce options and may comprise production constraints such as, forexample, production capacity for particular options. Demand planningengine 204 of server 112 may receive historical and forecast sales data230, such as, for example, past and projected demand data andmarketplace data from dealerships 170 and determine a demand plan,based, at least in part, on the received data.

Option planning engine 206 of server 112 may determine an option plan byassociating constraints with options of automobile option packagesaccording to options and configurations stored in configuration database220. Options data 222 of configuration database 220 may comprise dataidentifying available options associated with the make and models ofautomobiles. Each option may be associated with a particular automobileor one or more options may be associated with one or more automobiles,according to particular needs. Options may comprise selectable orconfigurable features, components, or configurations of automobiles. Forexample, options may comprise selection of an engine, transmission,wheels, color, seats, head lamps, quality of materials (such as interioror exterior finish options), brakes, tires, intake, exhaust, spoiler, orother components or systems of an automobile. Options may comprise theabsence or presence of any automotive component (such as, for example,having a spoiler or not having a spoiler) or may represent a particularconfiguration of any automotive component (such as, for example, havinga V8 engine versus a 4-cylinder engine). Options may comprise aparticular version or part number of a selected automotive component,which may vary based on geographical location, safety requirements,ruggedness, value (such as, for example, a premium versus an economymodel), or like considerations.

One or more of the options may have relationships that define variouscombinations and permutations of options in a finished automobile and/oran automotive component. These relationships may be defined by optionconstraints 224 of configuration database 220. Option constraints 224comprise limits and permissions for relationships between options, suchas limits to which options may occur together in a configuration andwhich options may not occur together in a configuration. Optionconstraints 224 may require that certain options are always found in anautomobile together, are never found in an automobile together, aredependent or independent of other options, must be found in specificratios in the automobile, and other like rules and constraints. Forexample, option constraints 224 may include, for example, that “premiumleather seating is only available with V-8 engine.” Therefore, anyoption for premium leather seating would be allowed only if the optionfor V-8 engine also occurred in the same configuration. Embodimentscontemplate any suitable option constraints 224, according to particularneeds. Option planning engine 206 may use options constraints 224 torefine the demand plan of the demand planning engine, such that, thedemand for options is compatible with supply chain constraints, such as,for example, option production constraints 244.

In addition, options constraints 224 may be assigned to optionsaccording to a hierarchy stored in hierarchy data 228. Hierarchy data228 may comprise a priority associated with each option such thatoptions with a higher priority are assigned to an automobile prior to anoption with a lower priority. For example, a demand target for an optionfor a V8 engine may have a higher priority than a demand target for anoption to include leather seats. If, for example, the demand for the V8engine was 100 vehicles and for leather seats was 80 vehicles, and allvehicles with a V8 engine must also have leather seats, then, the demandfor V8 engines will have a higher priority than the demand for leatherseats. Accordingly, the production planner 110 may determine that theproduction targets would be 100 vehicles with both the V8 engine optionand the leather seats option.

Each combination or permutation of automobile options may be termed aconfiguration stored as configuration data 226. A configuration maycomprise any collection of one or more automobile options, such asparticular lighting systems, engines, model type, wheels, or anycomponent or part of an automobile that may be configured, includingpermitted and disallowed configurations of each automobile.

Sales and operations planning engine 208 of server 112 may determine asales and operations plan based, at least in part, on option productionconstraints 242. According to embodiments, sales and operations planningengine 208 receives option production constraints 242 such as, forexample, constraints covering production limits on select options. Forexample, production limits may be maximum supply available per a definedtime horizon that is available to meet a particular demand volume.Embodiments contemplate that option production constraints 242 aredefined by a combination of logical operators.

According to embodiments, demand planning engine 204 and option planningengine 206 determine an unconstrained demand plan and option plan. Inone embodiment, sales and operations planning engine 208 receives anunconstrained demand and option plan as an input and then constrains theplan based on production limits and option compatibility. In addition,or as an alternative, the output of the sales and operations plan maycomprise a constrained demand and option plan which may not equal theunconstrained plan. In addition, the sales and operations plan may bevisible and applicable to all parts of supply chain network 100.

After the demand plan, option plan, and sales and operations plan aredetermined and production planning engine 202 generates a productionplan, master planner 210 of server 112 may generate a master plan andcommunicate the master plan to one or more third party logistics 130,suppliers 140, manufacturers 150, distributors 160, and dealerships 170to produce automobiles or automotive components according to the refinedmaster plan. As an example only and not by way of limitation, masterplanner 120 may place orders with one or more third party logistics 130,suppliers 140, manufacturers 150, and distributors 160 to produce orship automobile and automotive components according to the master planand may communicate to dealerships 170 the quantity and options ofautomobiles and automotive components that will be produced and the datethat the automobiles and automotive components will arrive atdealerships 170.

According to embodiments, the level of granularity in the master plan isdifferent than the production plan. Master planning may comprise, forexample, a buffer of an amount of material and an operation thatprocesses or transforms the material into an item with a set quantity.Embodiments of production planner 110 determine a production plancomprising a higher level of granularity than master planning. After theone or more inputs described above are received by production planner110, modeler 212 of production planner 110 may determine a productionplan utilizing one or more models 244.

Models 244 of the database may comprise any suitable model of anautomobile supply chain. According to some embodiments, the modelscomprise a network model comprising nodes and arcs where nodes representmanufacturers 150, automobile configurations, and markets and arcsrepresent the movement of automobile stock, as described in more detailbelow. According to other embodiments, models 244 comprise a mixedinteger linear programming MIP model with variable aggregation.According to further embodiments, models 244 comprise a well-structuredMIP model comprising three sub-models: a network production sub-model,an option capacity model, and a linking constraints model.

FIG. 3 illustrates an exemplary method 300 of automobile configurationplanning according to an embodiment. Although automobile configurationplanning is depicted as a linear process, one or more actions may beperformed in any order, combination, or repetitions to performautomobile configuration planning. For example, demand planning 302,option planning 304, and sales and operations planning 306 may compriseiterative processes that are performed multiple times in various orders,such that the demand plan, the option plan, and sales and operationsplan inform and refine each other according to sales forecast data 230,production capacity data 232, inventory data 234, time period data 236,manufacturer data 238, market data 240, models 232, option productionconstraints 244, options data 222, options constraints 224,configuration data 226, and hierarchy data 228. However, during demandplanning 302, option planning 304, and sales and operations planning306, the determined plans generally have few initial constraints, whichhelps generate plans directed to what the automobile manufacturer 150would like to build, not necessarily what they are able to build. As theplanning proceeds through further actions, more constraints are added orremoved to further align a desired plan with a feasible plan.

At action 302, demand planning engine 204 generates a demand plan from aglobal consolidated view of market demand and production requirements.Demand planning engine 204 may receive historical and forecast salesdata 230, option production constraints 244, and the like and generate ademand plan, which may include projected demand for one or moreautomobiles and automotive components. A demand plan may include apreliminary assessment of data received from dealerships 170, such as,for example, demand for types and quantities of automobiles andautomotive components. Production planner 110 may communicate thegenerated demand plan to the option planning engine 206 and sales andoperations planning engine 208.

At action 304, option planning engine 206 may determine the take ratesand volumes of automobiles and automotive components at the optionlevel. Option planning engine 206 may refine the demand plan accordingto the mix or the interaction between available automobile options.After action 304, production planner 110 may return to action 302 anditeratively refine the demand plan according to the option plan, such asanalyzing the available options and returning to the demand plan toalter take rate percentages. In addition, or in the alternative,production planner 110 may continue to action 306. At action 306, salesand operations planning engine 208 may generate a sales and operationplan optimized to fulfill market demand and generate forecast orders.For example, sales and operations planning engine 208 may refine theoption plan according to production capacity data 232, incrementally, sothat, for example, a sales and operation plan is substantially refinedaccording to the demand plan.

At action 308, production planning engine 202 communicates with thirdparty logistics 130, suppliers 140, manufacturers 150, distributors 160,dealerships 170 and/or other automotive supply chain entities togenerate a production plan that is optimized based on market demandwhile respecting constraints according to models 244. The productionplan may determine, for example, which automobiles are to be producedfor particular markets, at which manufacturers 150, for each of one ormore time periods. The production plan may be based on overall salesforecasts and respects supplier 140 and manufacturer 150 productioncapacity constraints. After the one or more inputs described above arereceived by production planner 110, modeler 212 of production planner110 may determine a production plan utilizing one or more models 244 asdescribed below.

At action 310, master planner 210 generates a master plan for productionof automobiles and automobile components. For example, master planner210 may generate a master plan that determines which automobiles andautomotive components will be produced during a specific time frame orplanning horizon, and the order or priority of the automobiles andautomotive components produced. As discussed herein, production planningengine 202 generates a production plan that is optimized based on marketdemand while respecting constraints according to models 244. The modelsdescribed below include: a network model, a MIP model with variableaggregation, and a well-structured MIP model.

Models 244 may include one or more constraints. For example, models 244may include one or more sales forecast constraints, production capacityconstraints, supplier and production capacity constraints for optiondefinition sets, and the like. A sales forecast constraint may compriserequiring that the inventory at the end of the previous planning periodplus the production during the current planning period minus theinventory at the end of the current planning equals the sales forecastfor the current planning period. The sales from a specific period may beshuffled to obtain what remains in stock so that the equation may berepresented by the previous stock added to what is produced andsubtracting what is sold is equal to the new stock for a given period.Production capacity constraints may comprise limiting the number ofvehicles of a vehicle model (sedan or SUV for example) produced at amanufacturer 150 by the capacity of each plant of the manufacturer 150.Production capacity constraints are defined for each manufacturingplant, each period, and each vehicle model. Supplier and productioncapacity constraints may be defined for option definition sets (ODS) andfor each period. Each of the constraints in models 244 may be defined byODS and time period. An ODS represents a particular automobilesub-configuration (for instance, a black sedan with a V8).

According to embodiments, ODS comprise rules that target some optionsfor one or more configurations. For example, some manufacturers 150 maybe restricted for a particular option, such as a big engine, whichlimits the amount of production for a particular configurationcomprising that option. ODS match automotive configurations and optionswhich are represented by a FDV. By way of further explanation an exampleis not given.

TABLE 1 Quantity Market Period Model 100 USA 1 Sedan 97 USA 2 Sedan 90USA 3 Sedan 100 USA 4 Sedan 50 USA 5 Sedan 65 USA 6 Sedan 120 USA 7Sedan 100 USA 8 Sedan 110 USA 9 Sedan 102 USA 10 Sedan

TABLE 1 illustrates a sales forecast for a single market for a singleautomobile model for ten upcoming time periods. Unlike other productionplanners that determine particular options to be produced, embodimentsof the current disclosure generate production plans based on high-levelsales forecasts comprising automobile, manufacturing plant, market,period information, such as from marketing or analysis from anautomobile manufacturer 150. According to the example illustrated, asedan is needed in a quantity of 100 automobiles for the USA market onperiod 1. After the high-level sales forecasts are received by theproduction planner, the production planner receives predefinedautomobiles, which may comprise, for example, a list of automobileconfigurations and a demand associated with particular options,configurations, or fully defined vehicles (FDV).

TABLE 2 FDV Sedan V8 RadioA Sunroof Sedan V8 RadioB Sunroof Sedan V8RadioA noSunroof Sedan V6 RadioA Sunroof Sedan V6 RadioB noSunroof SedanV6 RadioC Sunroof

As illustrated in TABLE 2, each of the FDV comprise codes that preciselydefine the configuration of each automobile. Each configuration may berepresented by a string of letters and numbers that identifyconfiguration options such as: automobile model, engine, radio, lights,color, braking system, or any other like automobile configurationoptions. Although the FDVs illustrated in TABLE 2 include options formodel (Sedan), engine (V8/V6), radio (RadioA, RadioB, and RadioC), andsunroof (Sunroof/No Sunroof), embodiments contemplate a FDV codecomprising any string of text, numbers, logical operators, or the likethat precisely define most or all of the options present on a vehicle.Additionally, the production planner may receive sales forecastsassociated with FDV, but, in most instances, the production planner willreceive sales forecasts associated with particular options orcombinations of options, which are defined by ODS.

ODS may be used to associate a FDV to a production option constraint.This constraint may be, for example, a capacity (upper bound) or adesired target. For example, in the following TABLE 3, various ODS haveproduction limits for various weekly time periods, according to thefollowing:

TABLE 3 2015/ 2015/ 2015/ 2015/ 2015/ ODS 2015/W36 W37 W38 W39 W40 W41Black SUV with V8 1327 1164 1406 1300 1406 1300 Any model with V6 46174049 4892 4524 4892 4524 Sedan with a sunroof 1616 911 1100 1017 11001017 but without spoiler SUV with a radio A 1750 1306 1630 1750 10581600 All sedans and pickups 652 1000 1000 175 1025 650 SUV with a 4cylinders 3800 3361 3240 3122 3323 3362

TABLE 3 illustrates ODS associated with the production capacities forparticular time periods. For example, according to TABLE 3, the ODS“Black SUV with V8” which represents all SUVs that are black and have aV8 engine, is limited to 1,327 automobiles in the 36th week of 2015 andto 1,164 automobiles in the 37th week of 2015. This option definitionset represents that, regardless of any configurations of availableoptions (and many options will fall under the ODS: Black SUV with V8),the production limit for all configurations whose FDV matches the ODS inthe chart is limited by the associated production capacity at eachlisted time period.

By way of a further example, in Row 4, the ODS “SUV with a radio A”represents one type of automobile and one type of radio. Any FDV thatcomprises SUV AND radio A will be associated with the productioncapacity constraint that the total of all SUVs with the radio A islimited to 3,800 automobiles in the 36th week of 2015 and 3,361 in the37th week of 2015. If, however, the radio A was used in another type ofautomobile, its production capacity would not be limited by theproduction capacity listed in the chart because the ODS would not matchthe FDV associated with that automobile configuration. Although theproduction capacity constraints in TABLE 3 are associated with timeperiods expressed in weeks, embodiments contemplate any suitable timeperiod, such as hours, days, months, quarters, years, or any othersuitable period of time.

According to an embodiment, the number of particular FDV entries for anautomobile manufacturer may exceed 1,000,000 entries. The large numberof entries creates scalability problems for many types of productionplanners. Other described mixed integer problem models may not bescalable to the number of options provided in an automobileconfiguration context. According to some embodiments, production planner110 uses variable aggregation to limit or reduce the number ofautomobile models analyzed by the model by constructing a novel datastructure that limits the number of automobile configurations. Thisnovel data structure is designed to improve the way a computer storesand retrieves data in memory.

According to some embodiments, variable aggregation may be used toaggregate many automobile configurations that end up as beingequivalent. As an example only and not by way of limitation, assumingamong all constraints targeting SUVs, the constraints fall into twocategories: (A) constraints that target SUVs; and (B) constraints thattarget black SUVs. It may then be possible to eliminate someconfigurations of SUVs in the model. Therefore, production planner 110may create two variables (or declinations of the FDVs): (1) the subsetof all non-black SUVs; and (2) the subset of all black SUVs. Therefore,for constraints relating to (A) SUVs, production planner 110 usesvariables (1) and (2) because this represents the integration of allSUVs (black and non-black), and, for constraints relating to (B) blackSUVs, production planner 110 uses only variable (2). This provides forconsidering all configurations of SUVs because the constraints arelimited to only that level of detail.

In other embodiments, if the constraints are defined in relation to SUVswith options for the radio, transmission, sunroof, and other likeoptions, then production planner 110 would construct additionaldeclinations of FDVs for the additional subgroups of SUVs, and the modelwould result in more variables. However, when the constraints arelimited to particular ODS, and even when there are many of them,production planner 110 will work faster by working with much less thanthe 1,000,000 FDVs, if they are not aggregated.

The following examples illustrate construction of an automobile supplychain network with automobile aggregation, according to an embodiment.

FIG. 4 illustrates a graphical representation of a network model 400 ofthe automobile supply chain network, according to an embodiment.According to embodiments, network model 400 represents one or morerelationships between variables and constraints using nodes and arrows.For example, vehicle model 402 may be produced by one or moremanufacturing plants 404 for one or more markets 406 during a firstplanning period 408 and a second planning period 410. Each of the shortarrows 412 a-412 l in the tree chart at the top represents one instanceof the variable x_(vehicle model,plant,market,period), which representsthe number of an automobile model at a particular manufacturing plantfor a particular market in a particular time period. A second variablein the model is the stock variable, S_(vehicle model,market,period). Thestock variable represents an amount of stock for an automobile model ata time period for a particular market. In the tree chart, the arrows 414a-414 b represent the stock variable, which may represent carryoverstock that is carried over from one period to another, such as from afirst period 408 to a second period 410. Each of the manufacturingplants 404 may have an initial stock during a first period 408, which isrepresented by the diagonal arrows 416 a-416 b. Each of themanufacturing plants 404 may also have sales of automobiles during eachperiod 408-410, which is represented by the diagonal arrows 418 a-418 d.

The vehicle model 402 may represent an imprecise configuration of anautomobile, because the stock constraints are not completely defined inthe automobile. The vehicle model 402 may represent an amount of anautomobile class (such as a sedan) in a specific market 406, but is notspecific to which variant of sedan it is, or the complete configurationof that automobile.

The following example illustrates graphically the generation of a linearprogramming problem according to an embodiment using the network model400 of the production plan. By way of example only and not by way oflimitation, assume that the production is planned for building a sedanvehicle model 402 for two time periods 408-410 (such as, for example,January and February) in two different markets 406 (USA and Canada).Further assume that there are two manufacturing plants 404, Plant A andPlant B. Plant A produces for both markets 406 (USA and Canada), andPlant B produces only for the Canadian market. Continuing with theexample, assume the sedan vehicle model 402 has three options, each withtwo choices for the option, according to the following:

TABLE 4 Class: Sedan Option Choice 1 Choice 2 Engine V8 4 cylinderSunroof Yes No Spoiler Yes No

This gives eight possible configurations:

TABLE 5 Sedan, V8, spoiler Sedan, 4 cyl., spoiler Sedan, V8, sunroof,spoiler Sedan, 4 cyl., spoiler, sunroof Sedan, V8 Sedan, 4 cyl. Sedan,V8, sunroof Sedan, 4 cyl., sunroof

Because the example of FIG. 4 only focuses on the sedan, without regardto the options, the vehicle model 402 can be represented using only oneautomobile class in the model: a sedan with any option. The totalproduction of the sedan will then be split between the eight possibleautomobile configurations in a post process.

Assume further that the sales forecast, the minimum and maximuminventory (Min-Max Stock Target), the initial inventory, and theproduction capacity (in vehicles) are only on the sedan vehicle model402 for the January and February planning periods 408-410 in the USA andCanadian markets 406, according to TABLES 6 and 7.

TABLE 6 January February USA Canada USA Canada Sales Forecast 650 300700 550 Min-Max Inventory Target 450-500 375-400 500-550 400-425 InitialInventory  50  25 N/A N/A

TABLE 7 January February Manufacturer PLANT A PLANT B PLANT A PLANT BProduction Capacity 500 400 600 500

FIG. 5 illustrates the flow of production of a single automobile modelthrough the exemplary network model of FIG. 4 with various constraintsindicated, according to an embodiment. In the graphical representationof a network model 400, sales for each market 404 for all sedanconfigurations are indicated by arrows 418 a-418 d pointing outward fromthe ellipses representing the markets 404 (USA and CAN). Sales indicatethe number of automobiles of all vehicle models 402 sold for each market406 in each time period 408-410. For example, sales for January for theUSA market are indicated as 650 automobiles, and for the Canadian marketas 300 automobiles. Sales for February are 700 automobiles for the USAmarket and 550 automobiles for the Canadian market.

In addition to sales, production capacity may also be added to themodel. Production capacity, represented by “Max” and a number beneatheach manufacturing plant 404, indicated by triangle labeled A and B(representing Plant A and Plant B), identify the maximum productioncapacity for all sedan configurations for each time period 408-410 andfor each manufacturing plant 406. For example, the maximum capacity forPlant A to build all sedan configurations is 500 automobiles in Januaryand 600 automobiles in February. Similarly, the maximum capacity forPlant B to build all sedan configurations is 400 automobiles in Januaryand 500 automobiles in February.

In addition to production capacity, the minimum and maximum stock foreach market 408-410 and manufacturing plants 404 may be added to thenetwork model 400. Minimum and maximum stock, represented by arrows 414a-414 b indicate a numerical range for the minimum and maximum number ofautomobiles that may be held in stock from one period to the next. Forexample, the number of sedans of all configurations that may be held instock between January and February for the USA market ranges between aminimum of 450 automobiles and a maximum of 500 automobiles. Similarly,the number of sedans of all configurations that may be held in stockbetween January and February for the Canadian market ranges between aminimum of 375 automobiles and a maximum of 400 automobiles.

In addition to the minimum and maximum stock, initial stock for eachmanufacturing plant 404 and market 406 may be added to the model.Initial stock, indicated by arrow 416 a-416 b pointing to each market406 in the January time period, indicates the number of automobiles thatare held in stock at each manufacturing plant 404 or market 406 at thebeginning of the planning horizon. For example, the amount of sedans ofall configurations that are initially in stock for January in the USAmarket is 50 automobiles. Similarly, the amount of sedans of allconfigurations that are initially in stock for January in the Canadianmarket is 25 automobiles.

At this point, production planner 110 may generate a mixed integerlinear program that may solve for the number of sedans that are to bebuilt by each manufacturing plant 404 and shipped to each market 406 foreach time period 408-410. After the one or more inputs described aboveare received by production planner 110, production planner 110 mayutilize a MIP model to determine a production plan. The MIP model maycomprise the decision variable, x_(vpmt), the volume of vehicle model402 v ∈ V produced at manufacturing plant 404 p ∈ P for market 406 m ∈ Mat time period 408-410 t ∈ T, and the following constraints (1)-(3):

$\begin{matrix}{{{{stock}_{m\;{l{({t - 1})}}} + {\sum\limits_{p}^{p}{\sum\limits_{v \in l}x_{vpmt}}} - {stock}_{mlt}} = {{sales}\mspace{14mu}{forecast}\mspace{14mu}{\forall m}}},{l \in L},t} & (1) \\{{{\sum\limits_{m}^{M}{\sum\limits_{v \in l}x_{vpmt}}} \leq {{plant}\mspace{14mu}{production}\mspace{14mu}{capacity}\mspace{14mu}{\forall p}}},{l \in L},t} & (2) \\{{{\sum\limits_{v \in {OD}}{\sum\limits_{p}{\sum\limits_{m}x_{vpmt}}}} \leq {{capacity}_{{({ODS})}t}{\forall{{ODS} \in {ODSs}}}}},t} & (3)\end{matrix}$

where, L represents the vehicle model set, and ODS represents an OptionData Set. The first constraint (1) of the MIP model depicted aboverepresents sales forecasts where the stock at the end of the last periodplus the production minus the stock at the end of the first periodequals the sales forecast. The sales from a specific period may beshuffled to obtain what remains in stock so that the equation may berepresented by the previous stock added to what is produced andsubtracting what is sold is equal to the new stock for a given period.

The second constraint (2) of the MIP model represents the productioncapacity constraints. The number of vehicles of a model (sedan or SUVfor example) produced at a manufacturing plant 404 is limited by thecapacity of this manufacturing plant 404. These constraints are definedfor each manufacturing plant 404, each period 408-410, and each vehiclemodel 402.

The third constraint (3) of the MIP model is based on an optiondefinition set (ODS). For each option definition set, there is asupplier/production capacity constraint. These constraints are definedfor each option definition set and for each period.

In this MIP model, all constraints may be soft by adding under and overslack variables. The slack variables may then be added into theobjective function and minimized with a descendant priority of: salesforecast, production capacities, option capacities, and initial stock.Although the MIP model is described with a descendent priority,embodiments contemplate a database structure that provides forreordering the priority of each variable or constraint according toparticular needs. For example, sales forecast is currently indicated ashaving a highest priority. However, by altering the formation of thedatabase that stores the sales forecasts, a different constraint may beplaced in a higher priority than the sales forecasts. In addition, or asan alternative, in order to produce the most automobiles as possible, apenalty may be associated with any result that produces less automobilesthan fixed by the MIP model.

Continuing with the same example above, assume that there is anadditional constraint comprising a sales forecast for a “sedan with aspoiler” that is 90 sedans with spoilers in January and 100 sedans withspoilers in February. According to the exemplary network model 400 thatwas just described, the automobile represents all configurations of asedan by a single vehicle model 402. Therefore, to add this constraint,the production planner 110 must split the single vehicle model 402 intotwo automobile classes: sedans WITH a spoiler and sedans WITHOUT aspoiler, according to the following:

TABLE 8 Class: Sedan With Spoiler Without Spoiler Sedan, V8, spoilerSedan, V8 Sedan, 4 cyl., spoiler Sedan, 4 cyl. Sedan, V8, sunroof,spoiler Sedan, V8, sunroof Sedan, 4 cyl., spoiler, sunroof Sedan, 4cyl., sunroof

With this new constraint that targets the option “spoiler,” the networkmodel 400 must now make a distinction between a sedan with a spoiler anda sedan without a spoiler. Four automobile configurations (the ones withspoilers) will be linked to the automobile “sedan with spoiler,” and theother four automobile configurations (the ones without spoilers) will belinked to the automobile “sedan without spoiler.” The total productionof “sedan with spoiler” will then be split between the four possibleautomobile configurations with spoiler in a post process. The sameprocess will be done with the “sedan without spoiler.” The additionalspoiler option production capacity constraint may be added to the modelas illustrated in the following figure.

FIG. 6 illustrates the flow of production of two automobile modelsthrough the exemplary network model 400 of FIG. 4 with variousconstraints indicated, according to an embodiment. To add the additionaloption production capacity, the automobile that was represented by asingle automobile icon is now split into two automobile icons 602-604:one that represents sedans with spoiler 602, and the other one thatrepresents sedans without spoiler 604. The market sales demand for thesedan with the spoiler indicated by arrows 606 a-606 c may be placed onthe arrows 412 a-412 c connecting the sedan with spoiler icon 602 to themanufacturing plant 404 that can produce the sedan with spoiler in thefirst period 408. Similarly, the market sales demand for the sedan withthe spoiler indicated by arrows 606 d-606 f may be placed on the arrows412 m-412 o connecting the sedan with spoiler icon 602 to themanufacturing plant 404 that can produce the sedan with spoiler in thesecond period 410. Here, the number of sedans with spoiler is indicatedas a maximum of 90 automobiles for January, and a maximum of 100automobiles for February.

Once all constraints are modeled, production planner 110 may generate anoptimization solution based on known amounts (i.e. sales, productioncapacity, minimum and maximum stock, initial stock, and/or optionproduction capacity). Production planner 110 determines the flow on eachproduction flow arrow 412 a-412 x in the above graphic to satisfy theconstraints arrows 414 a-414 b, 416 a-416 b, 418 a-418 d, and 606 a-606f, while respecting the conservation of flow (i.e. that the flowentering a node must equal the flow leaving the node). To perform thisdetermination, production planner 110 transforms the chart into a linearprogram and solves it with, for example, a simplex algorithm, accordingto one or more mathematical models, as explained in detail above. By wayof a further example of a graphical network model 400 consider thefollowing.

FIG. 7 illustrates the flow of production of two automobile models withthree configurations through the exemplary network model 400 of FIG. 4with various constraints indicated, according to an embodiment. A firstautomobile configuration 702 is a sedan model with a spoiler, the secondautomobile configuration 704 is a sedan model with upgraded wheels, andthe third vehicle configuration 706 is a hatchback model. The trianglesrepresent automobile manufacturing plants 404, the ellipses representdestination markets 406, and the arrows 412 a-412 y connecting theautomobile configurations 702-706, manufacturing plants 404, and markets406 represent the allocation of automobiles among the variousmanufacturing plants 404 and markets 406. The tree chart is also dividedinto two periods, a first period 408 (Period 1) on the left side, and asecond period 410 (Period 2) on the right side.

During the first period 408, Period 1, the arrow 412 a connecting thefirst automobile configuration 702 (sedan model with spoiler) to Plant Arepresents that Plant A will produce 50 automobiles of the firstconfiguration. The arrow 412 b connecting the first automobileconfiguration 702 to Plant B represents that Plant B will produce 70automobiles of the first configuration. Similarly, Plant A will produce80 automobiles of the second configuration 704 (sedan model withupgraded wheels) and Plant C will produce 20 automobiles of the secondconfiguration 704. Also, Plant B will produce 100 automobiles of thethird configuration 706 (hatchback).

The arrows 412 f-412 n connecting manufacturing plants 404 to markets406 represent the automobile configurations shipped from thosemanufacturing plants to the markets indicated. For example, theuppermost arrow 412 f connecting Plant A to the USA market indicatesthat 20 automobiles of the first configuration 702 will be shipped fromPlant A to the USA market. Similarly, the network model 400 indicatesthat 30 automobiles of the first configuration 702 will be shipped fromPlant A to the Canadian market. Continuing with the example, Plant Bwill produce 70 automobiles of the first configuration 702 for theCanadian market and no automobiles of the first configuration 702 forthe USA market. Plant A will also produce 50 automobiles of the secondconfiguration 704 for the USA market and 30 vehicles for the Canadianmarket. Plant C will produce 10 automobiles of the second configuration704 for the USA market and also produce 10 automobiles for the Canadianmarket. Finally, Plant B will produce 75 automobiles of the thirdconfiguration 706 for the Canadian market and 25 automobiles for theMexican market.

Also, some amount of initial stock may be present in Period 1 for theUSA market for the first automobile configuration. This is indicated by“Initial Stock” and an arrow 416 a pointing at the USA market for thefirst automobile configuration 702. The network model 400 indicates that50 automobiles were sold from this first time period by arrow 418 a, andthe arrow 414 a from the USA ellipse in Period 1 to the USA ellipse inPeriod 2 represents unsold stock (30 automobiles) that is carried overfrom Period 1 408 to Period 2 410.

For Period 2, a similar production plan is determined based on theautomobile configurations 702-706, manufacturing plants 404, and thedestination markets 406, and including any unsold stock from Period 1.For example, in the second period 410, Period 2, 40 automobiles of thefirst automobile configuration 702 will be produced by Plant A and 10automobiles of the first automobile configuration 702 will be producedby Plant B. Plant C will produce 20 automobiles of the secondconfiguration 704, and Place B will produce 80 automobiles of the thirdconfiguration. 706. Similar to Period 1, production planner willdetermine automobile allocation from each manufacturing plant 404 todifferent destination markets 406 based on particular automobileconfigurations 702-706. For example, 20 automobiles of the firstconfiguration 702 will be shipped from Plant A to the USA, and 20automobiles of the first configuration will be shipped from Plant A tothe Canadian market. The allocation of the remaining automobiles isindicated. After all constraints are input into the model, productionplanner 110 may determine a production plan using the MIP modeldescribed and comprising the number of automobiles to produce atparticular plants shipped to particular regions during particular timeperiods.

Turning to a separate model, production planner 110 may determine aproduction plan using a well-structured MIP model which comprises threesub-models: a network production sub-model, an option capacitysub-model, and a linking constraints sub-model.

The network production sub-model may comprise, for example, a suitablemixed integer linear program model consistent according to thefollowing. For example, given the decision variables, x_(lpmt), which isthe volume of the automobile model l (l ∈ L) (such a sedan, SUV, orother like automobile models) produced at manufacturing plant p (p ∈ P)to market m (m ∈ M) at period t (t ∈ T); and w_(tpt)/z_(tpt), which arethe under/over slack of production of automobile model l, for plant p atperiod t; and the parameter c_(lpt)/d_(lpt), which is the under/overpenalty of slack of production constraints of model l, for plant p atperiod t, the production network model may comprise the followingobjective (4) and constraints (5)-(9):

$\begin{matrix}{{\min\;{\sum\limits_{m \in M}{\sum\limits_{l \in l}{\sum\limits_{t \in T}\left( {{c_{lpt}w_{lpt}} + {d_{lpt}z_{lpt}}} \right)}}}}{{subject}\mspace{14mu}{to}\text{:}}} & (4) \\{{{{stock}_{m\;{l{({t - 1})}}} + {\sum\limits_{p}^{P}x_{lpmt}} - {stock}_{mlt}} = {{sales}\mspace{14mu}{forecast}\mspace{11mu}{\forall m}}},{l \in L},t} & (5) \\{{{{\sum\limits_{m \in M}x_{lpmt}} + w_{lpt} - z_{lpt}} = {{production}\mspace{14mu}{capacity}\mspace{14mu}{\forall{p \in P}}}},{l \in L},{t \in T}} & (6) \\{{minStock}_{mlt} < {stock}_{mlt} \leq {maxStock}_{mlt}} & (7) \\{x_{lpmt},w_{lpt},{z_{lpt} \geq 0}} & (8) \\{{x_{lpmt},w_{lpt},{z_{lpt} \in {\mathbb{N}}}}{{{where}\mspace{14mu} L} = {{vehicle}\mspace{14mu}{model}\mspace{14mu}{set}}}} & (9)\end{matrix}$

The objective (4) of the production network sub-model minimizes thepenalty associated with the slack to satisfy the sales forecast andminimize the violation of the production capacity. The constraintsinclude the sales forecast (5) must be equal to the initial stock at thebeginning of a planning period, stock_(ml(t-1)), plus the production ofthe automobile model during the production period, Σ_(p) ^(P) x_(lpmt),minus the stock remaining at the end of the production period,stock_(mlt). A further constraint (6) includes setting productioncapacity an automobile model equal to the production at a particularplant, Σ_(m ∈M) x_(lpmt), plus or minus any slack, w_(lpt)-z_(lpt).Also, all stock, stock_(mlt), is constrained (7) to be between theminimum stock, minStock_(mlt), and maximum stock, maxStock_(mlt). Also,all decision variables are non-negative (8) and natural numbers (i.e.zero and positive integers) (9).

Although the network production sub-model accounts for production, salesforecast, and stock constraints, it fails to address option capacityconstraints. For example, continuing with the example of FIGS. 4-5,assume that an additional constraint of a sales forecast for a sedanwith a spoiler is 90 automobiles in January and 100 automobiles inFebruary. According to the exemplary network model 400 that wasdescribed, the network model 400 of FIGS. 4-5 fails to account fordifferent configurations of a sedan. For example, the sedans maycomprise the eight configurations of sedans WITH a spoiler and sedansWITHOUT according to TABLE 8. Instead of continuing with the networkmodel 400 of FIG. 6, production planner 110 may employ an optioncapacity sub-model to model the configurations of the vehicle model.

According to embodiments, the network model 400 does not efficientlymodel automobile options because, owing to the large number of possibleconfigurations, the network model 400 may be too large to calculate (theRAM requirements have exceeded 256 GB in some models) for even amoderate-sized automobile supply chain network 100. Therefore, eventhough production planner 110 may use the production network sub-modelto determine how many sedans may be produced, it cannot determineautomobile options, such as how many sedans with spoilers should beproduced and how many sedans without spoilers should be produced.

Instead, production planner 110 models option capacity production andFDV using the option capacity sub-model. Markets are not targeted incapacity constraints so these may be merged in the option capacitysub-model. In other words, the production network sub-model considersonly automobile models (such as, for example, sedans and SUVs), and theoption capacity sub-model considers the FDV, such as, for example,particular sedan configurations, including the sedan with particularconfigurations of spoilers, engines, or sunroofs, as indicated in TABLE8.

According to embodiments of the option capacity sub-model, productionplanner 110 models option capacity production and FDV with the decisionvariables, y_(vpt), which is the volume of the vehicle (or class) v, (v∈ V), produced at plant p (p ∈ P), at period t (t ∈ T);u_(ODSt)/O_(ODSt), which are the under/over slack of capacity ODS atperiod t; and parameters, a_(ODSt)/b_(ODSt), which are the penalties forthe under/over slack of capacity ODS at period t. Some FDVs cannot beproduced in certain manufacturing plants. If an automobile model v canbe produced in manufacturing plant p, then, this may indicated in theoption constraint model by v ∈ Vp. An automobile class may be anysuitable configuration of an automobile or automobile component, such as“sedan with a spoiler,” being one automobile class, and “sedan without aspoiler,” being another automobile class. Although particular examplesare given, automobile class may comprise any configuration of automobileor automotive components, according to particular needs.

According to embodiments, the option capacity sub-model comprises thefollowing objective (10) and constraints (11)-(13):

$\begin{matrix}{{\min\;{\sum\limits_{{ODS} \in {ODSs}}{\sum\limits_{t \in T}\left( {{a_{ODSt}u_{ODSt}} + {b_{ODSt}o_{ODST}}} \right)}}}{{subject}\mspace{14mu}{to}\text{:}}} & (10) \\{{{{\sum\limits_{p \in P}{\sum\limits_{v \in {{ODS}\bigwedge v} \in V_{p}}y_{vpt}}} + u_{ODSt} - o_{ODSt}} = {{capacity}_{ODSt}\mspace{11mu}{\forall{{ODS} \in {ODSs}}}}},{t\mspace{14mu}{\forall T}}} & (11) \\{y_{vpt},u_{ODSt},{o_{ODSt} \geq 0}} & (12) \\{{y_{vpt},u_{ODSt},{o_{ODSt} \in {\mathbb{N}}}}{{{where}\mspace{14mu}{ODS}} = {{option}\mspace{14mu}{defintion}\mspace{14mu}{set}}}} & (13)\end{matrix}$

The objective (10) of the option capacity sub-model minimizes theviolation of the capacity constraints for ODS by the penaltiesassociated with the slack. The constraints include the option capacityconstraint, capacity_(ODSt), (11), and that all decision variables arenon-negative (12) and natural numbers (13).

To generate a production plan, the production network sub-model and theoption capacity sub-model may be joined by the linking constraintssub-model to generate a complete well-structured MIP model. According toembodiments, the linking constraint comprises:

$\begin{matrix}{{{{\sum\limits_{v \in l}y_{vpt}} - {\sum\limits_{m \in M}x_{lpmt}}} = {0\mspace{14mu}{\forall{l \in L}}}},{p \in P},{t{\forall T}}} & (14)\end{matrix}$

The linking constraint sub-model comprises a constraint (14) that joinsthe production network sub-model to the option capacity sub-model bysetting as equal to zero the difference between volume of an automotivemodel (such as, for example, the sedan) that is produced at plant p atmarket m, at time period t, x_(lpmt), equal to the production of theautomobile class (such as, for example, “sedans with spoilers,” and“sedans without spoilers) at plant p, at period t, y_(vpt). Becausemarket m is not taken into account in the option capacity sub-model, thelinking constraint sums the volume of the automobile or automotivecomponent over all markets.

When the network production sub-model, the option capacity sub-model,and the linking constraints sub-model are joined, production planner maygenerate the following complete well-structured MIP model of minimizingthe objective function (15) subject to constraints (16)-(22):

$\begin{matrix}{{{\min\;{\sum\limits_{{ODS} \in {ODSs}}{\sum\limits_{t \in T}\left( {{a_{ODSt}u_{ODSt}} + {b_{ODSt}o_{ODSt}}} \right)}}} + {\sum\limits_{l \in L}{\sum\limits_{p \in P}{\sum\limits_{t \in T}\left( {{c_{lpt}w_{lpt}} + {d_{lpt}z_{lpt}}} \right)}}}}{{subject}\mspace{14mu}{to}\text{:}}} & (15) \\{{{{stock}_{m\;{l{({t - 1})}}} + {\sum\limits_{p \in P}x_{lpmt}} - {stock}_{mlt}} = {{sales}\mspace{14mu}{forecast}\mspace{14mu}{\forall m}}},{l \in L},t} & (16) \\{{{{\sum\limits_{m \in M}x_{lpmt}} + w_{lpt} - z_{lpt}} = {{production}\mspace{14mu}{capacity}\mspace{14mu}{\forall{p \in P}}}},{l \in L},{t \in T}} & (17) \\{{minStock}_{mlt} \leq {stock}_{mlt} \leq {maxStock}_{mlt}} & (18) \\{{{{\sum\limits_{p \in P}\;{\sum\limits_{v \in {{ODS}\bigwedge v} \in {Vp}}y_{vpt}}} + u_{ODSt} - o_{ODSt}} = {{capacity}_{ODSt}\mspace{11mu}{\forall{{ODS} \in {ODSs}}}}},{t\mspace{14mu}{\forall T}}} & (19) \\{{{{\sum\limits_{v \in l}y_{vpt}} - {\sum\limits_{m \in M}x_{lpmt}}} = {0\mspace{14mu}{\forall{l \in L}}}},{p \in P},{t\mspace{14mu}{\forall T}}} & (20) \\{x_{lpmt},y_{vpt},{stock}_{mlt},u_{ODSt},w_{lpt},{z_{lpt} \geq 0}} & (21) \\{x_{lpmt},y_{vpt},{stock}_{mlt},u_{ODSt},o_{ODSt},w_{lpt},{z_{lpt} \in {\mathbb{N}}}} & (22)\end{matrix}$

The solution of the complete well-structured MIP model represents theproduction plan for the automotive supply chain network including theconstraints for sales forecasts, production capacity, minimum andmaximum stock, and the capacity for particular options, as explainedabove in connection with the production network sub-model and the optioncapacity sub-model.

FIG. 8 illustrates a linear equation matrix 800 of the completewell-structured MIP model of the automotive supply chain network,according to an embodiment. The matrix of the linear equation matrix(Ax=b) illustrates the production network sub-model with sideconstraints with the production and the min-max stock constraints, thelinking constraints, and the option capacity sub-model.

FIG. 9 illustrates the structure 900 of the linear equation matrix 800of the complete well-structured MIP model of the automotive supply chainnetwork, according to an embodiment. As can be seen by the non-zerovalues in the structure 900, the complete well-structured MIP model iswell-structured. Based on the stock, production constraints, linkingconstraints, and the production of the production network sub-modelequal to the production of the option capacity sub-model, the completewell-structured MIP model comprises a well-structured model, as can beseen by the diagonal shape of the matrix, the minimal rows, thesparseness, and only having values of −1 and 1 in the matrix. Matriceswith this structure may be solved quickly with even a commercial solver,such as, for example, a SIMPLEX solver. Additionally, the linearrelaxation is close to the integer solution since it is a network modelwith side constraints, which may be solved easily, as well.

In fact, the model is able to efficiently solve in approximately twentyminutes, which is substantially less time than traditional methods, witha 0.01% gap, an automobile supply chain production problem comprising,approximately, 400,000 vehicles, 77 vehicle models, 22 plants, 48 timeperiods, 725 regions, 4,608 production constraints (model/plant/period),309,000 sales forecasts (model/region/period), and 120,192 optioncapacity constraints (more than 10000 options).

To further illustrate the operation of production planner 110, considerthe following regional sales forecast.

TABLE 9 Model REGION Sep-15 Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Mar-16SEDAN USA 7592 7400 7321 8681 4215 4881 6266 SEDAN CAN 14522 12067 1379211644 15688 15203 19307 SEDAN MEX 12784 10372 9195 14316 8268 9966 14328PICKUP USA 483 837 889 1243 196 327 436 PICKUP CAN 2516 3275 3629 27273346 3251 3949 PICKUP MEX 1605 1041 869 1016 1260 749 1416 ELEC USA 11526 13 9 15 16 18 ELEC CAN 955 1178 1197 1115 802 757 1130 ELEC MEX 852895 960 1748 937 995 1200 SUV USA 9052 6893 7036 7072 6560 5866 4312 SUVCAN 11571 9009 9132 8543 10093 9741 13919 SUV MEX 7926 5940 5584 58584683 5739 7577

TABLE 9 represents a regional sales forecasts associated with aparticular model for a particular region, for particular time periods.For example, a SEDAN model in the American region is needed in theamounts of 7,592 for September 2015 and 7,400 in October 2015. Thisinput comprises a first constraint on the model.

TABLE 10 AUGUST SEPTEMBER Plant Model 2015/W35 2015/W36 2015/W372015/W38 2015/W39 2015/W40 B SEDAN 27 120 150 150 150 90 C ELEC 61 374445 446 483 270 C SEDAN 390 2264 2676 2682 2908 1620 D SUV 1152 45974990 6115 5655 3375 A SEDAN 768 4170 4992 4992 1664 2796 A PICKUP 2131156 1392 1392 464 696

TABLE 10 illustrates plant production capacities for particular modelsassociated with particular time periods. Here, the SEDAN model may onlybe produced by the plant B in the amount of 120 in the 36th week of2015. This input comprises a further constraint on the model.

TABLE 11 Model REGION Sep-15 Oct-15 Nov-15 Dec-15 Jan-16 SEDAN USA 93079606 9422 5954 6658 SEDAN CAN 22535 24331 25510 27182 27546 SEDAN MEX12941 14720 15865 11396 13581 PICKUP USA 614 705 938 290 358 PICKUP CAN6690 6784 6423 6591 6630 PICKUP MEX 1558 1507 1725 1675 1441 ELEC USA 34 4 5 7 ELEC CAN 1658 1766 1564 1215 1239 ELEC MEX 1215 1496 1914 12531302 SUV USA 18053 17938 15289 12010 9922 SUV CAN 13811 14030 1440514661 15694 SUV MEX 5522 5507 5653 4590 5359

TABLE 11 illustrates a minimum stock associated with each model for aparticular region at particular time periods. For example, the SEDANmodel is limited to a minimum of 9,307 automobiles in the Americanregion for September of 2015, and 9,606 in October of 2015. Thiscomprises a further constraint on the model.

TABLE 12 Model REGION Sep-15 Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 SEDANUSA 11634 12008 11777 7443 8322 8978 SEDAN CAN 28169 30414 31887 3397834433 34869 SEDAN MEX 16176 18400 19831 14245 16976 18604 PICKUP USA 767881 1172 362 448 481 PICKUP CAN 8362 8480 8029 8239 8287 8540 PICKUP MEX1948 1884 2156 2094 1801 2227 ELEC USA 4 5 5 6 9 8 ELEC CAN 2073 22071955 1519 1549 1778 ELEC MEX 1519 1870 2392 1566 1627 1636 SUV USA 2256622422 19111 15012 12403 10617 SUV CAN 17264 17537 18006 18326 1961720881 SUV MEX 6902 6884 7066 5737 6699 7263

TABLE 12 illustrates a maximum stock associated with each model for aparticular region at particular time periods. For example, the SEDANmodel is limited to a maximum of 11,634 automobiles in the Americanregion for September of 2015, and 12,008 in October of 2015. Thiscomprises a further constraint on the model.

TABLE 13 Model REGION Total SEDAN USA 10176 SEDAN CAN 20463 SEDAN MEX9726 PICKUP USA 444 PICKUP CAN 5731 PICKUP MEX 1561 ELEC USA 95 ELEC CAN1061 ELEC MEX 690 SUV USA 16267 SUV CAN 15945 SUV MEX 8080

TABLE 13 illustrates an initial stock associated with each model for aparticular region at the beginning of the production planning period.The amount of automobiles indicated in the total column represents theamount of initial stock on-hand at the particular region at thebeginning of the production planning period. For example, the amount ofSEDAN models in the American region at the beginning of the planningperiod is 10,176 automobiles.

TABLE 14 2015/ 2015/ 2015/ 2015/ 2015/ ODS 2015/W36 W37 W38 W39 W40 W41Black SUV with V8 1327 1164 1406 1300 1406 1300 Any model with V6 46174049 4892 4524 4892 4524 Sedan with a sunroof 1616 911 1100 1017 11001017 but without spoiler SUV with a radio A 1750 1306 1630 1750 10581600 All sedans and pickups 652 1000 1000 175 1025 650 SUV with a 4cylinders 3800 3361 3240 3122 3323 3362

TABLE 14 illustrates constraints for ODS associated with particular timeperiods. As explained in detail above, these constraints may compriseproduction capacity constraints or other limits on the total number ofcomprising FDV that match the ODS listed in the above chart. Forexample, the total number of Black SUVs with V8 is 1,327 in the 36thweek of 2015 and 1,164 in the 37th week of 2015. After all constraintsare input into the model, as explained in greater detail above,production planner 110 may determine a production plan comprising thenumber of automobiles to produce at particular plants shipped toparticular regions during particular time periods.

The following table illustrates a simplified production plan for an SUVmodel.

TABLE 15 Plant Market Period Volume A USA 1 15 A USA 2 20 B USA 1 0 CCAN 1 76 C CAN 2 112 C MEX 3 34

TABLE 15 illustrates an exemplary production plan for an automobileconfiguration according to an embodiment. A production plan for theautomobile configuration FDV1 is illustrated. The FDV1 may represent forexample, a SUV model, a V8-4.2 engine, a RADA radio, no all-wheel drive(AWD), and a black color. The production plan generated by productionplanner 110 may indicate that the FDV1 model should be built inparticular volumes, at particular plants, in particular markets, forparticular periods based on overall sales volume forecast whilerespecting plant and supplier capacity. For example, the production planillustrated in the above figure indicates that Plant A should product avolume of 15 automobiles for the USA market in a first period, and 20automobiles in a second period. Plant B should product no automobiles,and Plant C should produce 76 automobiles for the Canadian market in thefirst time period, and 112 automobiles for the Canadian market in thesecond time period. Plant C should also produce 34 automobiles in athird period for the Mexican market. Although particular plants,markets, periods, and volumes are illustrated, embodiments contemplateany suitable number or types of plants, markets, periods, or volumesaccording to particular needs.

The production plan based on the FDV1 automobile configuration issimpler than previous attempts at generating a production plan.According to embodiments, the solution does not target all the optionsin an automobile configuration. Many of the options will have beenaggregated together through declination of FDVs, as described above.

Reference in the foregoing specification to “one embodiment”, “anembodiment”, or “some embodiments” means that a particular feature,structure, or characteristic described in connection with the embodimentis included in at least one embodiment of the invention. The appearancesof the phrase “in one embodiment” in various places in the specificationare not necessarily all referring to the same embodiment.

While the exemplary embodiments have been shown and described, it willbe understood that various changes and modifications to the foregoingembodiments may become apparent to those skilled in the art withoutdeparting from the spirit and scope of the present invention.

What is claimed is:
 1. A method, comprising: modeling two or morepredefined automobile configurations and one or more constraintsassociated with an automobile supply chain as a mixed integer linearprogramming problem; determining a production plan for the automobilebased, at least in part, on the two or more predefined automobileconfigurations; and comparing the difference between a current inventorylevel of an automobile and a forecasted production level for theautomobile in the production plan and sending, by production planner toautomated machinery, instructions to cause the automated machinery toretrieve an amount of the automobile equal to the forecasted productionlevel minus the current inventory level and to move the amount of theautomobile to an inventory location of the automobile.
 2. The method ofclaim 1, further comprising: representing the one or more predefinedautomobile configurations by an alphanumeric string; and aggregatingvariables of the predefined automobile configurations by one or moreoption definition sets.
 3. The method of claim 2, wherein the one ormore constraints comprise one or more option production constraintsrelated to the capability of one or more manufacturers and one or moreproduction constraints.
 4. The method of claim 3, wherein the one ormore production constraints comprises production capacity for one ormore options.
 5. The method of claim 4, wherein the mixed integer linearprogramming problem comprises a well-structured mixed integer linearprogramming problem comprising a network production sub-model, an optioncapacity sub-model; and the network production sub-model is linked tothe option capacity sub-model by a linking constraint sub-model.
 6. Themethod of claim 4, wherein the mixed integer linear programming problemcomprises a mixed integer linear programming problem model with variableaggregation.
 7. A system, comprising: a production planner comprising aprocessor and a memory, the production planner configured to: model twoor more predefined automobile configurations and one or more constraintsassociated with an automobile supply chain as a mixed integer linearprogramming problem; determine a production plan for the automobilebased, at least in part, on the two or more predefined automobileconfigurations; and compare the difference between a current inventorylevel of an automobile and a forecasted production level for theautomobile in the production plan and send to automated machinery,instructions to cause the automated machinery to retrieve an amount ofthe automobile equal to the forecasted production level minus thecurrent inventory level and to move the amount of the automobile to aninventory location of the automobile.
 8. The system of claim 7, whereinthe production planner is further configured to: represent the one ormore predefined automobile configurations by an alphanumeric string; andaggregate variables of the predefined automobile configurations by oneor more option definition sets.
 9. The system of claim 8, wherein theone or more constraints comprise one or more option productionconstraints related to the capability of one or more manufacturers andone or more production constraints.
 10. The system of claim 9, whereinthe one or more production constraints comprises production capacity forone or more options.
 11. The system of claim 10, wherein the mixedinteger linear programming problem comprises a well-structured mixedinteger linear programming problem comprising a network productionsub-model, an option capacity sub-model; and the network productionsub-model is linked to the option capacity sub-model by a linkingconstraint sub-model.
 12. The system of claim 10, wherein the mixedinteger linear programming problem comprises a mixed integer linearprogramming problem model with variable aggregation.
 13. The system ofclaim 11, wherein the linking constraint sub-model comprises aconstraint that joins the production network sub-model to the optioncapacity sub-model by setting as equal to zero the difference betweenvolume of an automobile model that is produced at a particular plant fora particular market at a particular time period equal to the productionof an automobile class at the particular plant at the particular timeperiod, summed over all markets.
 14. A non-transitory computer-readablemedium comprising software, the software when executed configured to:model two or more predefined automobile configurations and one or moreconstraints associated with an automobile supply chain as a mixedinteger linear programming problem; determine a production plan for theautomobile based, at least in part, on the two or more predefinedautomobile configurations; and compare the difference between a currentinventory level of an automobile and a forecasted production level forthe automobile in the production plan and send to automated machinery,instructions to cause the automated machinery to retrieve an amount ofthe automobile equal to the forecasted production level minus thecurrent inventory level and to move the amount of the automobile to aninventory location of the automobile.
 15. The non-transitorycomputer-readable medium of claim 14, wherein the software is furtherconfigured to: represent the one or more predefined automobileconfigurations by an alphanumeric string; and aggregate variables of thepredefined automobile configurations by one or more option definitionsets.
 16. The non-transitory computer-readable medium of claim 15,wherein the one or more constraints comprise one or more optionproduction constraints related to the capability of one or moremanufacturers and one or more production constraints.
 17. Thenon-transitory computer-readable medium of claim 16, wherein the one ormore production constraints comprises production capacity for one ormore options.
 18. The non-transitory computer-readable medium of claim17, wherein the mixed integer linear programming problem comprises awell-structured mixed integer linear programming problem comprising anetwork production sub-model, an option capacity sub-model; and thenetwork production sub-model is linked to the option capacity sub-modelby a linking constraint sub-model.
 19. The non-transitorycomputer-readable medium of claim 17, wherein the mixed integer linearprogramming problem comprises a mixed integer linear programming problemmodel with variable aggregation.
 20. The non-transitorycomputer-readable medium of claim 18, wherein the linking constraintsub-model comprises a constraint that joins the production networksub-model to the option capacity sub-model by setting as equal to zerothe difference between volume of an automobile model that is produced ata particular plant for a particular market at a particular time periodequal to the production of an automobile class at the particular plantat the particular time period, summed over all markets.